Brief Announcement: Stabilizing Consensus with the Power of Two Choices

Abstract

Consensus problems occur in many contexts and have therefore been extensively studied in the past. In the original consensus problem, every process initially proposes a value, and the goal is to decide on a single value from all those proposed. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process irrevocably commits to a final value but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. In other words, we are searching for a self-stabilizing algorithm for the consensus problem. Coming up with such an algorithm is easy without adversarial involvement, but we allow some adversary to continuously change the states of some of the nodes at will. Despite these state changes, we would like the processes to arrive quickly at a common value that will be preserved for as many time steps as possible (in a sense that almost all of the processes will store this value during that period of time). Interestingly, we will demonstrate that there is a simple algorithm for this problem that essentially needs logarithmic time and work with high probability to arrive at such a stable value, even if the adversary can perform arbitrary state changes, as long as it can only do so for a limited number of processes at a time.